Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial

Abstract

We show that scale-invariant special Kahler geometries whose generic r-complex-dimensional abelian variety fiber is isomorphic (completely split) or isogenous (completely iso-split) as a complex torus to the product of r one-dimensional complex tori have constant ${\tau }^{ij}$ modulus on the Coulomb branch, i.e., are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kahler geometries, which, in turn, is relevant to the classification of possible 4-dimensional N=2 supersymmetric superconformal field theories.

arXiv comment39 pages, 3 figures. Corrections to various arguments in sections 2 and 3. Results unchanged

References in corpus (9)

• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Special Kahler Manifolds
• N=2 supersymmetric dynamics for pedestrians
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs